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/********************* */
/*! \file witness_form.cpp
** \verbatim
** Top contributors (to current version):
** Andrew Reynolds
** This file is part of the CVC4 project.
** Copyright (c) 2009-2021 by the authors listed in the file AUTHORS
** in the top-level source directory and their institutional affiliations.
** All rights reserved. See the file COPYING in the top-level source
** directory for licensing information.\endverbatim
**
** \brief The module for managing witness form conversion in proofs
**/
#include "smt/witness_form.h"
#include "expr/skolem_manager.h"
#include "theory/rewriter.h"
namespace CVC4 {
namespace smt {
WitnessFormGenerator::WitnessFormGenerator(ProofNodeManager* pnm)
: d_tcpg(pnm,
nullptr,
TConvPolicy::FIXPOINT,
TConvCachePolicy::NEVER,
"WfGenerator::TConvProofGenerator",
nullptr,
true),
d_wintroPf(pnm, nullptr, nullptr, "WfGenerator::LazyCDProof"),
d_pskPf(pnm, nullptr, "WfGenerator::PurifySkolemProof")
{
}
std::shared_ptr<ProofNode> WitnessFormGenerator::getProofFor(Node eq)
{
if (eq.getKind() != kind::EQUAL)
{
// expecting an equality
return nullptr;
}
Node lhs = eq[0];
Node rhs = convertToWitnessForm(eq[0]);
if (rhs != eq[1])
{
// expecting witness form
return nullptr;
}
std::shared_ptr<ProofNode> pn = d_tcpg.getProofFor(eq);
Assert(pn != nullptr);
return pn;
}
std::string WitnessFormGenerator::identify() const
{
return "WitnessFormGenerator";
}
Node WitnessFormGenerator::convertToWitnessForm(Node t)
{
NodeManager* nm = NodeManager::currentNM();
SkolemManager* skm = nm->getSkolemManager();
Node tw = SkolemManager::getWitnessForm(t);
if (t == tw)
{
// trivial case
return tw;
}
std::unordered_set<TNode, TNodeHashFunction>::iterator it;
std::vector<TNode> visit;
TNode cur;
TNode curw;
visit.push_back(t);
do
{
cur = visit.back();
visit.pop_back();
it = d_visited.find(cur);
if (it == d_visited.end())
{
d_visited.insert(cur);
curw = SkolemManager::getWitnessForm(cur);
// if its witness form is different
if (cur != curw)
{
if (cur.isVar())
{
Node eq = cur.eqNode(curw);
// equality between a variable and its witness form
d_eqs.insert(eq);
Assert(curw.getKind() == kind::WITNESS);
Node skBody = SkolemManager::getSkolemForm(curw[1]);
Node exists = nm->mkNode(kind::EXISTS, curw[0], skBody);
ProofGenerator* pg = skm->getProofGenerator(exists);
if (pg == nullptr)
{
// it may be a purification skolem
pg = convertExistsInternal(exists);
if (pg == nullptr)
{
// if no proof generator is provided, we justify the existential
// using the WITNESS_AXIOM trusted rule by providing it to the
// call to addLazyStep below.
Trace("witness-form")
<< "WitnessFormGenerator: No proof generator for " << exists
<< std::endl;
}
}
// --------------------------- from pg
// (exists ((x T)) (P x))
// --------------------------- WITNESS_INTRO
// k = (witness ((x T)) (P x))
d_wintroPf.addLazyStep(
exists,
pg,
PfRule::WITNESS_AXIOM,
true,
"WitnessFormGenerator::convertToWitnessForm:witness_axiom");
d_wintroPf.addStep(eq, PfRule::WITNESS_INTRO, {exists}, {});
d_tcpg.addRewriteStep(
cur, curw, &d_wintroPf, true, PfRule::ASSUME, true);
}
else
{
// A term whose witness form is different from itself, recurse.
// It should be the case that cur has children, since the witness
// form of constants are themselves.
Assert(cur.getNumChildren() > 0);
if (cur.hasOperator())
{
visit.push_back(cur.getOperator());
}
visit.insert(visit.end(), cur.begin(), cur.end());
}
}
}
} while (!visit.empty());
return tw;
}
bool WitnessFormGenerator::requiresWitnessFormTransform(Node t, Node s) const
{
return theory::Rewriter::rewrite(t) != theory::Rewriter::rewrite(s);
}
bool WitnessFormGenerator::requiresWitnessFormIntro(Node t) const
{
Node tr = theory::Rewriter::rewrite(t);
return !tr.isConst() || !tr.getConst<bool>();
}
const std::unordered_set<Node, NodeHashFunction>&
WitnessFormGenerator::getWitnessFormEqs() const
{
return d_eqs;
}
ProofGenerator* WitnessFormGenerator::convertExistsInternal(Node exists)
{
Assert(exists.getKind() == kind::EXISTS);
if (exists[0].getNumChildren() == 1 && exists[1].getKind() == kind::EQUAL
&& exists[1][0] == exists[0][0])
{
Node tpurified = exists[1][1];
Trace("witness-form") << "convertExistsInternal: infer purification "
<< exists << " for " << tpurified << std::endl;
// ------ REFL
// t = t
// ---------------- EXISTS_INTRO
// exists x. x = t
// The concluded existential is then used to construct the witness term
// via witness intro.
Node teq = tpurified.eqNode(tpurified);
d_pskPf.addStep(teq, PfRule::REFL, {}, {tpurified});
d_pskPf.addStep(exists, PfRule::EXISTS_INTRO, {teq}, {exists});
return &d_pskPf;
}
return nullptr;
}
} // namespace smt
} // namespace CVC4
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